CEE 379
HW#9
PROFESSOR EBERHARD
AUTUMN 2007
PROBLEM 1:
a.) Determi ne the degree of kinem atic indeterminac y.
θ
B
+ D
B
+ θ
C
+ θ
D
= 4
b.) Beam Siffness Matrices For Beams AB, BC, CD
Member AB : Elemental Stiffness Matrix
Input Properties E (ksi) I (in
4
)X
N
(in.)
YN
(in.) X
F
(in.) Y
F
(in.) d (in.)
29000 1500 0 0 264 0 15.6
Calculated Properties
DOF 1 DOF 2 DOF 3 DOF 4
L (in.) EI (k/*n
2
.)
q
Ny'
28.37 3744. 83 -28.37 3744.83
d
Nx
DOF 1
264.00 43500000.00
m
NFz'
3744.83 659090.91 -3744.83 329545.45
d
Ny
DOF 2
cos(theta) sin(theta)
q
Fy'
-28.37 -3744.83 28.37 -3744.83
d
Fx
DOF 3
1.00 0.00
m
Fz'
3744.83 329545.45 -3744.83 659090.91
d
Fy
DOF 4
Member BC : Elemental Stiffness Matrix
Input Properties E (ksi) I (in
4
)X
N
(in.)
YN
(in.) X
F
(in.) Y
F
(in.) d (in.)
29000 1500 264 0 462 0 15.6
Calculated Properties
DOF 3 DOF 4 DOF 5 DOF 6
L (in.) EI (k/*n
2
.)
q
Ny'
67.25 6657. 48 -67.25 6657.48
d
Nx
DOF 3
198.00 43500000.00
m
NFz'
6657.48 878787.88 -6657.48 439393.94
d
Ny
DOF 4
cos(theta) sin(theta)
q
Fy'
-67.25 -6657.48 67.25 -6657.48
d
Fx
DOF 5
1.00 0.00
m
Fz'
6657.48 439393.94 -6657.48 878787.88
d
Fy
DOF 6
Member CD : Elemental Stiffness Matrix
Input Properties E (ksi) I (in
4
)X
N
(in.)
YN
(in.) X
F
(in.) Y
F
(in.) d (in.)
29000 1500 462 0 660 0 15.6
Calculated Properties
DOF 5 DOF 6 DOF 7 DOF 8
L (in.) EI (k/*n
2
.)
q
Ny'
67.25 6657. 48 -67.25 6657.48
d
Nx
DOF 5
198.00 43500000.00
m
NFz'
6657.48 878787.88 -6657.48 439393.94
d
Ny
DOF 6
cos(theta) sin(theta)
q
Fy'
-67.25 -6657.48 67.25 -6657.48
d
Fx
DOF 7
1.00 0.00
m
Fz'
6657.48 439393.94 -6657.48 878787.88
d
Fy
DOF 8
c.) Express Equi librium Equatio ns at each DOF
Assemble Glo bal Stiffness Matrix , K (k/in)
DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6 DOF 7 DOF 8
28.37
3744.83
-28.37
3744.83
0.00
0.00
0.00
0.00
DOF 1
D
A
3744.83
659090.91
-3744.83
329545.45
0.00
0.00
0.00
0.00
DOF 2
θ
A
-28.37
-3744.83
95.62
2912.65
-67.25
6657.48
0.00
0.00
DOF 3
D
B
3744.83
329545.45
2912.65
1537878.79
-6657.48
439393.94
0.00
0.00
DOF 4
θ
B
0.00
0.00
-67.25
-6657.48
134.49
0.00
-67.25
6657.48
DOF 5
D
C
0.00
0.00
6657.48
439393.94
0.00
1757575.76
-6657.48
439393.94
DOF 6
θ
C
0.00
0.00
0.00
0.00
-67.25
-6657.48
67.25
-6657.48
DOF 7
D
D
0.00
0.00
0.00
0.00
6657.48
439393.94
-6657.48
878787.88
DOF 8
θ
D
BLUE = FREE DOF
Partition Fr ee Stiffness Matrix , K
11 (k/in)
DOF 4 DOF 5 DOF 6 DOF 8
1537878.79
-6657.48
439393.94
0.00
DOF 4
θ
B
-6657.48
134.49
0.00
6657.48
DOF 5
D
C
439393.94
0.00
1757575.76
439393.94
DOF 6
θ
C
0.00
6657.48
439393.94
878787.88
DOF 8
θ
D
=
=
K
11
(K
ff)
=
